Inverse Square Law
This is the definition of the Inverse Square Law: *Basically, it means that as a release of energy (usually an explosion) expands further outwards, the intensity of the released energy decreases. This is due to the total amount of released energy from the explosion is spread out over a wider surface area. **This is also the reason why an object further away from an explosion will end up being less damaged in comparison to an object that is closer to it. Because as the explosion expands further and further outwards from its epicenter, the less intense the energy from that explosion will be when it finally hits that object. *The simplied formula for this is = (area of the object being affected) x (surface area of the radiated energy) When should we use Inverse Square Law? Here are some uses where this particular law may apply. *Finding the resulting yield of an explosion based on the energy required to destroy an object from a measurable distance. *Finding the object's durability from withstanding an explosion from a measurable distance. *The equation of the Inverse Square Law is... Why is it used? Something that is overlooked when dealing with Destructive Ability-related feats is the surface area of the attack that makes direct contact with the targer. For example, the energy that is applied in a person's footsteps would theoretically be more than enough to kill a very small insect, such as an ant. However, the surface area of the foot is much larger in comparison to the surface area of the ant itself. Thus, what ends up happening is that the ant does not take the full brunt of the energy applied from the footstep, and the ant may possibly survive. However, if a finger is pressed on the exact same ant, the applied energy from the finger press would cause the ant to be crushed, as the area ratio between the finger and the ant is not nearly as large as in comparison to the ratio between someone's foot and the exact same ant. This would also apply to the example of explosions, especially when the explosion hits an object that is located from a considerable amount of distance. Since the intensity of an explosion's energy decreases as the radius of the explosion increases further away from its epicenter, 'Finding energy based on something destroyed within an explosion' Here is an example calculation for the energy required to destroy Neptune, the furthest planet away from our solar system from an explosion that starts from the Sun. 1. Find the durability required to destroy the object. *In this case, we will use the GBE of Neptune, which is the minimum energy required to unbind everything that composes Neptune so that it does not attach itself back together. Here are the stats of Neptune, which yields the GBE of it using this calculator. *Planetary Diameter = 49244km *Surface Gravity = 11.15m/s^2, or 1.1369g (g = gravity of Earth, so the surface gravity of Neptune would be 1.1369x higher in this case) *GBE = 1.668e34 Joules *This step applies to all objects that need to be destroyed by an explosion that happens at a distance. Just find the energy required to destroy that object first. Since we now have the minimum energy required to destroy Neptune, we then find the surface area of Neptune that makes direct contact with the explosion. 2. Surface area of object *Next, we find the surface area of the object that makes contact with the explosion. In this case, the object is shaped like a sphere. *Radius of sphere (Neptune) = 49244km divided by 2 = 24622km *Radius in meters = 24,622,000 m *Surface area of a sphere: A''' = 4*Pi*(radius^2) where radius = radius of planet in meters = 7.618e15m^2 *You have to use divide the surface area of the object in question by 2, as only half the surface of the object makes contact with the explosion, with the other half being on the other side. *Surface area of object making contact = 3.809e15m^2. Now that we have the surface area of the object making contact (Neptune in this case), We need to find the distance of the oject. '''3. Distance between the epicenter of explosion and the object *To find the distance from where the explosion starts all the way to the point where the explosion hits the object...Actually, in this case you can Google the distance between the Sun and the Neptune. But for other cases you may have to do some research to find that distance. *In this case, you also need to add the radius of the Sun alongside the radius of the explosion travelling all the way to Neptune. Thus we get... **(radius of the sun = 695700km) + (distance to Neptune = 4,300,000,000 km) = 4,300,695,700 km. But just use the distance to Neptune instead. It's close enough. 4. Surface area of the shape of explosion *Next, you find the surface area of the explosion's overall shape when it directly hits Neptune. Note that due to the shape of the expanding explosion being shaped similarly to a sphere (as the explosion spreads outwards omnidirectionally/in all directions), you need to use the surface area equation for spheres, again. *Surface area of explosion when the radius reaches from epicenter to Neptune = A = A''' = 4*Pi*(radius^2) *Radius = 4.3e9km, of 4.3e12m *Area = 2.32e26 m^2 We got the surface area of explosion when it expands to Neptune. '''5. Ratio of surface area of explosion compared to the object *Surface area of Neptune = 3.809e15m^2 (1) *Surface area of explosion = 2.32e26 m^2 (2) *Ratio = (2)/(1) = ~60,908,374,901x *By the point the explosion reaches the distance to Neptune, the intensity of the explosion becomes 60.908 billion times less intense in comparison to its epicenter. *Mutiply the ratio that you got with the GBE of Neptune, as the explosion still managed to destroy Neptune from that distance. *Explosion energy required to destroy Neptune at end of border = 6.0908e10 x 1.668e34 Joules = 1.016e45 Joules *Explosion energy required to destroy Neptune at end of border = 1.016e45 Joules, or 2.428e35 Tons of TNT Note: To convert from joules of energy to TNT equivalent, divide the number of joules by 4.184e9. Inverse Square Law and Destructive Ability *Note that the values listed on the Destructive Ability page uses the Inverse Square Law method to find the results for the values required for Solar System level to Multi-Solar System level. *Since the method of "destruction" on this level of scale is almost always portrayed as a continuously expanding explosion that destroys any objects managing to come in contact with it. *It is also the reason why this Wiki doesn't consider other methods such as mass-energy equivalence and gravitational binding energy when it comes to the destruction of solar systems, galaxies, etc. **This entire section is rather poorly worded, so any suggestions for improvement would be welcome. Category:Calculation Instructions